Let
be a complete discrete valuation field with ring of integers
and algebraically
closed residue field
of characteristic
.
Let
be a smooth proper geometrically connected curve of genus
with
if
. Assume
that
does not have good reduction and that it obtains good reduction over a Galois extension
of degree
. Let
be the smooth
model of
.
Let
.
In this article, we provide information on the regular model of
obtained by desingularizing the wild quotient singularities of the quotient
. The most
precise information on the resolution of these quotient singularities is obtained when the
special fiber
is ordinary. As a corollary, we are able to produce for each odd prime
an infinite class of wild quotient singularities having pairwise
distinct resolution graphs. The information on the regular model of
also allows us to gather
insight into the
-part
of the component group of the Néron model of the Jacobian of
.
Keywords
model of a curve, ordinary curve, cyclic quotient
singularity, wild ramification, arithmetical tree,
resolution graph, component group, Néron model
